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🌍 Russian Peasant, Lattice & Egyptian Multiplication Explained
Different cultures found different ways to multiply. Learning a second method is not just fun: it shows why multiplication works, and gives children a way to check their answers.
Russian peasant: only halving and doubling
Write the numbers side by side. Halve the left (drop any remainder) and double the right, until the left reaches 1. Cross out rows where the left is even, then add the right column.
| Halve | Double | |
|---|---|---|
| 18 | 25 | ✘ even |
| 9 | 50 | ✔ |
| 4 | 100 | ✘ |
| 2 | 200 | ✘ |
| 1 | 400 | ✔ |
50 + 400 = 450, and 18 × 25 = 450. It works because halving writes 18 in binary (16 + 2), the same idea computers use.
Lattice (gelosia): carry only once
For 23 × 45, draw a 2 × 2 grid with a diagonal in each box. Fill each box with a small product split into tens and ones: 2 × 4 = 08, 2 × 5 = 10, 3 × 4 = 12, 3 × 5 = 15. Then add along the diagonals from the bottom right: 5, then 1 + 0 + 2 = 3, then 1 + 1 + 8 = 10 (write 0, carry 1), then 0 + 1 = 1. Read off 1035.
Egyptian doubling
From the Rhind Papyrus (about 1550 BCE). For 13 × 21, list doubles of 21: 1 → 21, 2 → 42, 4 → 84, 8 → 168. Since 13 = 8 + 4 + 1, add 168 + 84 + 21 = 273.
Trachtenberg × 6
Put a 0 in front, then work right to left: each digit plus half of its right-hand neighbour, plus 5 if the digit is odd. 342 × 6: 2 → 2; 4 + 1 = 5; 3 + 2 + 5 = 10 (write 0, carry 1); 0 + 1 + 1 = 2. Answer: 2052.
Chisanbop: a calculator on your hands
A Korean finger method: on the right hand each finger is 1 and the thumb is 5; on the left hand each finger is 10 and the thumb is 50. It works exactly like abacus beads, so it is a great bridge for young children.
Why learn more than one method?
Each method breaks a number into parts in a different way: binary, place value, diagonals. Seeing the same answer appear from different routes builds real understanding, and a second method is the best way to check the first.
Try all of these in the World Methods section of the BeadBop app, with step-by-step animations and practice questions.
Quick answers
How does Russian peasant multiplication work?
Halve the left number and double the right until the left is 1, cross out rows where the left number is even, and add what remains on the right. It works because the halving writes the left number in binary.
Is lattice multiplication taught in schools?
It is not part of most Indian school syllabi, but many teachers use it to show place value, because every small product is written down and carrying happens only once, at the end.
What is the Trachtenberg system?
A set of fast mental multiplication rules created by Jakow Trachtenberg in the 1940s. Each multiplier (×5, ×6, ×7, ×11, ×12 and so on) has its own simple rule applied digit by digit.